Step 1: Prepare the Salmon

1. Pat the salmon fillets dry with paper towels and season both sides with salt and pepper.
2. Dredge each fillet lightly in flour, shaking off any excess.

Step 2: Sear the Salmon

1. Heat the olive oil and butter in a large skillet over medium heat.
2. Add the salmon fillets, skin-side up, and sear for 3–4 minutes until golden brown.
3. Flip the fillets and cook for another 3–4 minutes, or until the salmon is cooked through and flakes easily. Remove the salmon from the skillet and set aside.

Step 3: Make the Sauce

1. In the same skillet, add the minced garlic and sauté for 30 seconds until fragrant.
2. Pour in the white wine (or chicken broth) and let it simmer for 2–3 minutes, scraping up any browned bits from the bottom of the skillet.
3. Stir in the heavy cream, lemon juice, capers, salt, and pepper. Bring the mixture to a gentle simmer.
4. Stir in the grated Parmesan cheese and whisk until melted and the sauce thickens slightly. If the sauce is too thick, add a splash of chicken broth to adjust the consistency.

Step 4: Combine and Serve

1. Return the salmon fillets to the skillet, spooning the sauce over each piece. Allow the salmon to warm through for 1–2 minutes.
2. Garnish with fresh parsley and serve immediately over pasta, rice, or steamed vegetables.